Thanks to Albany, luxury developers may dodge property taxes in exchange for building — or at least funding — some affordable housing. But with $1 billion a year in uncollected taxes, are these really good deals for NYC?

At 90 stories, it will be tallest residential tower in the city. With sweeping views of downtown Manhattan and Central Park, the $1.5 billion building is one of the most coveted addresses; a 14,000-square-foot penthouse already sold for more than $90 million.

The sweetheart deal for One57 developer Extell, tucked into a larger housing bill at the behest of Assembly Speaker Sheldon Silver and signed by Gov. Cuomo, is under investigation by Albany’s anti-corruption Moreland Commission.

It’s also drawn renewed scrutiny to the 421-a tax exemption, a controversial program that dates back to the 1970s when the city began offering breaks to spur residential development.

The city lost out on a whopping $1 billion in property taxes last fiscal year under the 421-a program.

In exchange, the developers are suppose to set aside 20% of their units for affordable housing or fund affordable housing in another way.

But is the amount of money New York loses to these exemptions, which could go to programs that benefit the entire city, really offset by a relatively small number of apartments with lower rents?

Critics say no.

“Our city spends $1 billion every year on these kinds of subsidies, with little affordable housing to show for it. These valuable public resources should be used to keep New York affordable for middle- and low-income New Yorkers,” said Brooklyn Councilman Brad Lander.

One57 isn’t even providing new affordable housing under its deal. The development was not supposed to be eligible for a 421-a exemption because of its location in a high-density area of Manhattan.

But the project was one of five Manhattan developments that got special dispensation to apply for the exemption when they were tucked into the housing bill.

Four of the five developers contributed heavily to Cuomo and political and campaign committees in 2012, according to a report by the Metropolitan Council on Housing.

Cuomo raked in $150,000 in donations from Extell and three of the other developers in 2012, the report found.

“Whether that was foul play or not, we must stop these giveaways and use the money effectively to solve our affordable-housing problem,” said Jaron Benjamin, executive director of the Metropolitan Council on Housing.

So far, only two of the five developers have applied to the city’s Housing Preservation and Development agency for the 421-a break. A rental development at 113 Nassau St. is slated to have 20% of the apartments as affordable housing in order to get the exemption.

There will be no bargain basement living at One57, where the $90 million penthouse went to hedge funder Bill Ackman. A second penthouse sold for about the same amount. The building will have 94 condominiums, 38 rentals and a Park Hyatt hotel at its base.

If approved by the city, the individual condo owners would avoid property taxes for 10 years, though the amount of savings hasn’t been calculated yet by the city. By one estimate, each of the two penthouse owners would save more than $1 million in taxes over 10 years.

In order to qualify for the tax break, the city left it up to Extell to spend whatever it wanted to subsidize affordable housing. Extell bought “negotiable certificates” generated when another developer built three affordable-housing projects with a total 297 units in The Bronx. The projects were completed several years ago.

Extell’s $5.9 million contribution in effect paid for about 63 units.

The certificate program was a way for market-rate developers to fund affordable housing but was discontinued in 2007 as part of a series of reforms of the 421-a program.

But Extell and other developers can continue to buy certificates that are still available for sale.

An Extell spokeswoman would not comment on the pending tax exemption and would only say that “One57 during construction and the first 10 years of operations will generate over $2.5 billion of economic benefit to New York City and state in the form of taxes and economic investment.”

Paul Korngold, a lawyer representing developers, argued that without these deals, no middle-class person could afford to rent an apartment — particularly not in Manhattan.